I agree with Antonio. Besides pronunciations and writing, I think the dialects sound very different too. Modal words are more often used in Taiwan, for example, 啊 啦 etc. Taiwanese people speak in a very tender way. As you hear it, you can feel the difference, or as you watch the Taiwan dramas.

Personally I think there are lots of differences. For example, the writing. In China people use simplified Chinese while in Taiwan traditional Chinese is used. Some characters may be alike, though many are totally different and can not be recognized by one another. Another difference is the accent. The way the Taiwanese talk are considered quite distinct of the standard Mandarin. Also, the way to type out characters on phone or computers are totally different.

some pronunciations and handwriting taiwanese use traditional chinese while we use simple chinese

Accents are different, even in China, there are still many kinds of accents. In writting, Taiwanese use troditional Mandarin while simplified Mandarin is used in China. TM is hard to write but more logical, on contrary, SM is easy to write but not that logical. Besides, Taiwan has other language that used in the mass, Taiwanese, which is transformed from Southern Min(閩南；min3 nan2). It's hard to explain in English, but fujian's southern min language is able to communicate yet distinct with tainwanese southern min language(Taiwanese). Around 80% taiwan citizen know Tainwanese so we use a lot of taiwanese words mixed with chinese, it also makes difference from China.

First, the pronouciation is different. More people can understand the Mandarin in mainland. By the way, the Mandarin in Beijing I think it's the most standard one. Second, writing is different. The people in Taiwan write traditional Chinese character, but in mainland, we write simplified character which is more popular.